IMO Shortlist 1999 problem N5
Dodao/la:
arhiva2. travnja 2012. Let
be positive integers such that n is not divisible by 3 and
. Prove that there exists a positive integer
which is divisible by
and the sum of its digits in decimal representation is
.
%V0
Let $n,k$ be positive integers such that n is not divisible by 3 and $k \geq n$. Prove that there exists a positive integer $m$ which is divisible by $n$ and the sum of its digits in decimal representation is $k$.
Izvor: Međunarodna matematička olimpijada, shortlist 1999